The Heisenberg category of a category

Ádám Gyenge; Clemens Koppensteiner; Timothy Logvinenko

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arXiv · 2105.13334

The Heisenberg category of a category

Ádám Gyenge·Clemens Koppensteiner·Timothy Logvinenko

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Abstract

Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group of the original category. We also define a 2-categorical analogue of the Fock space representation of the Heisenberg algebra. Our construction generalises and unifies various categorical Heisenberg algebra actions appearing in the literature. In particular, we give a full categorical enhancement of the action on derived categories of symmetric quotient stacks introduced by Krug, which itself categorifies a Heisenberg algebra action proposed by Grojnowski.

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Ádám Gyenge, Clemens Koppensteiner, Timothy Logvinenko. 2021-05-27. The Heisenberg category of a category. https://arxiv.org/abs/2105.13334

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